Calculator using TypeScript type system

calc.ts

type Compare<A extends number, B extends number, X extends any[]=[], Y extends any[]=[]> = X['length'] extends A
  ? Y['length'] extends B ? 0 : -1
  : Y['length'] extends B ? 1 : Compare<A, B, [any, ...X], [any, ...Y]>

type IsLower<A extends number, B extends number> = Compare<A, B> extends -1 ? true : false;
type IsHigher<A extends number, B extends number> = Compare<A, B> extends 1 ? true : false;

type CreateArray<N extends number, A extends any[]=[]> = A['length'] extends N ? A : CreateArray<N, [any, ...A]>

type Add<A extends number, B extends number> = [...CreateArray<A>, ...CreateArray<B>]['length'];

type Subtract<A extends number, B extends number,> = CreateArray<B> extends infer ArrB extends any[] ? (
    ArrB['length'] extends 0 ? A : (
        ArrB extends [a: infer BX, ...b: infer BY] ? (
            CreateArray<A> extends [a: infer AX, ...b: infer AY] ? (
                Subtract<AY['length'], BY['length']>
            ) : never
        ) : never
    )
) : never;

type Multiply<A extends number, B extends number, R extends number = 0> = B extends 0 ? R
    : Add<A, R> extends infer XR extends number ?
        Multiply<A, Subtract<B, 1>, XR> :
        never;

type Divide<N extends number, M extends number, V extends number = 0, P extends number=0> = IsHigher<Multiply<V,  M>, N> extends true
  ? P : (
    Add<V, 1> extends infer X extends number ? 
        Divide<N, M, X, V>
    : never
  );

type Operator = '+' | '-' |'*' | '/';

type Calc<A extends number, Op extends Operator, B extends number> = Op extends '+' ? (
    Add<A, B>
) : (
    Op extends '-' ? (
        Subtract<A, B>
    ) : (
        Op extends '*' ? (
            Multiply<A, B>
        ) : Divide<A, B>
    )
)

type FivePlusTwo = Calc<5, '+', 2>;
type FiveMinusThree = Calc<5, '-', 3>;
type FiveTimesFour = Calc<5, '*', 4>;
type EightByFour = Calc<8, '/', 4>;